No, in practice, because the top two contenders are likely to be two who are actually popular.
Plurality voting typically finds an equilibrium where the "two most popular" candidates are both extremists.
http://zesty.ca/voting/sim/ has some nice plots showing how the two most popular candidates change from centrists under approval voting to relative extremists under plurality. (I advocate IRV because when in doubt the voting system should degenerate into random chaos. 1 person in 100 shouldn't be a big enough margin to secure power as a principle either)
Strategic voting doesn't just happen once, people apply a strategy over multiple elections and can exert influence before the election even happens. In a two-party system the party in charge knows they'll be punished for egregious transgressions - even by some of their core supporters - leading to opposite policies, whereas in multi-party if one party is caught cheating for instance they know voters will defect to a party with similar policies. The parties also act strategically.
If they want to use a satisfaction model it should be lifetime satisfaction, how well the system represented people overall. This may be basically impossible to model without a complete understanding of human nature, but it matters in the real world; if your country gets overthrown or ultimately makes poor decisions it doesn't matter how satisfied you were with the candidates at one point in time.
Personally I think the Condorcet methods are not that difficult to explain. The various ways of resolving not perfectly clear situations are a little involved, but everything else makes perfect sense. I built a visualisation a few years ago that created a directed graph of results, and then analysed the strongly connected components.
Having said that, I hadn't come across STAR before and I think it makes a fair amount of sense. Any of these high quality methods are enormously better than those used in lots of countries.
To the voter, no. It is just a ranked choice/ordinal system (which is why people get mad at IRV being called RCV). Just rank your candidates in order of preference. People naturally understand this, yes. BUT that's not what people typically mean when they says the system is hard to understand. What matters is transparency and how easy it is to tabulate the votes. Actually this is where all ordinal systems fall in comparison to cardinal systems. In cardinal systems just just sum some columns (in STAR you have to do this twice). But in ordinal systems you have to do many rounds of counting and eliminations. Look at the current NYC mayoral race. We have only one round counted and they have like 10 more days before round 2 (which is funny because IRV results typically follow the first round results, we expect Adams to win). So look into tabulating Schulze or Ranked Pairs. Condorcet methods require you to run n^2 election because you have to run every pair. Now consider contested elections like what is going on in Arizona. The more complex of a counting system is the more either end can be abused (the original vote or the verification). If it is sufficiently complex a group will easily be able to justify foul play regardless of actual proof because the evidence against the claim is nuanced.
So yes, it isn't hard to explain to voters, but it is difficult to explain how you count the votes. But VSE is only one metric. Like you pointed out max(STAR) is only slightly less than max(condorcet) but min(STAR) has a decent gap over min(condorcet), which also matters. The smaller range on STAR suggests it is more resilient to strategic voting (or voter manipulation). But cardinal systems are not only easy to explain to voters but it is also easy to explain how votes are counted. I should also note that Approval/Score/STAR are monotonic and will not spoil elections (IRV increases spoilage where cardinals decrease). I'll also suggest that if you're a data person you should be in favor of Score and STAR because they are more expressive than any ordinal system because the distance between your preferences isn't constant and thus we can get more fine grained data on voter preference.
If we only look at the VSE metric, condorcet wins, but what makes voting complicated is that this isn't the only metric.
Those virtual elections are not difficult to run (electronically) or explain though: "we use the ballots to work out for every person how they would do in a one on one election against each other person".
And the process for running the elections is straightforward too - count the number of ballots where one person appears higher in the list than the other person. There's no room for argument here, unless you're arguing about the ballots, which is something you can do with any system.
All of that stuff seems pretty straightforward to me.
Now, it is the case that the various ways of resolving situations where you have cycles is somewhat complex. I think that's just because those situations are genuinely complex, but there are things that can be done here to choose a relatively explainable one and work out good ways to visualize and explain it.
Finally, while cardinal systems can express the distance between preferences, there are ways an ordinal system can express things hard for a cardinal system. In an ordinal system you can allow a ballot not to include someone and have that mean 'no preference' between that person and all other candidates (perhaps because of lack of knowledge), while in an cardinal system an unscored person would have to be counted as having an actual score. There's also the question whether preferences really are consistent enough for a cardinal system to accurately reflect them - you might like X three times more than Y, and two times more than Z, but does that necessarily mean that you like Z one and a half times more than Y? Personally I also think there's a big difference between preferences between two candidates you'd be happy to win and candidates you actively don't want to win, and I don't think that difference can be captured by just making a scalar larger - not that ordinal approaches capture this either.
But what I do want to stress is that cardinal systems are _easier_ than condorcet. I actually use approval frequently (it is also extremely natural). One case is how to solve where to eat as a group. It is infinitely scalable and you can just keep adding places as you think of them. If you reach a unanimous decision you stop, if you exhaust the list you take the maximal (baring strong preferences, which makes it kinda score but this works out naturally). I think from this example it should be pretty clear that it is much harder to do this sort of voting using any ranking system (nor is it scalable and is very computationally expensive to add new items).
It is often missed, especially by nerds (I fall in this camp too, I used to prefer Condorcet over cardinal), how important the transparency aspect of the voting system is. Arizona nailed the lid shut for me. If we're looking at it we're really not losing much VSE by using STAR over RP, but we do also gain a lot on every other metric (including spoilage, ease, transparency, and resistance to strategy). VSE isn't the only metric that matters and we shouldn't make large sacrifices in other metrics to gain a minute optimization in it.
> while in an cardinal system an unscored person would have to be counted as having an actual score.
This isn't necessarily true. You can modify cardinal ballots just like you do ordinal (the exact example you gave is not the theoretically perfect ordinal so I'm not sure why you compare to theoretically perfect cardinal). In practice people don't rate every candidate. In ranking you could effectively say that unranked candidates have a minimal score (and you are able to reduce the number of rounds through this, but comes with added complexity).
As to making the scale larger, yes this is correct that an infinitely large scale better encodes information. But there is a balance between that and simplicity. 10 is extremely effective. 5 is more than enough. But even 2 (approve/disapprove) seems to work out pretty well (aka "good enough").
To me, any voting method dependent on software is a non-starter. A full paper trail is much easier to audit
To me, it's a hard choice that cardinal systems don't force you to make.
The lesson of voting theory is to avoid ranked voting methods.
> It looks like it's a metric constructed to justify Range-ish voting systems, a la Warren Smith's Bayesian regret models.
Bayesian regret wasn't constructed to justify score voting (formerly known as range voting). Smith correctly used a utilitarian social welfare function, and just happened to find that score voting did best. This was by no means a given.
Indeed, the VSE calculations (conducted by a different mathematician, Jameson Quinn), used some different assumptions, and had STAR voting, 321 voting, and even certain Condorcet methods, beating score voting in some circumstances.
> It degenerates to pretty much the same problem as Plurality voting
You have this literally backwards.
http://scorevoting.net/BulletBugaboo https://electionscience.org/library/irv-degrades-to-pluralit...
> You just can't model strategy this naively.
It was modeled in a very sophisticated way, not "naively". The VSE figures even used all kinds of variations, e.g. asymmetric strategy where one side strategizes more than the other.
> And Range/Score voting is even more extreme: you can vote strategically there even knowing nothing about other people's preferences. Just always use extreme values (0 and 100).
And even if you do, it still gets better results.
> Borda gets a bad rap in these comparisons. It's not a good system, but the likelihood that "strategic voting" will backfire horribly means that in all likelihood, voters would not pursue those strategies.
That doesn't make any sense. Strategy, by definition, is a move which has a positive expected value. You seem to be conflating "bad aggregate performance under strategy" with "bad individual performance for a voter who uses strategy", which is deeply wrong.
Exactly. Voting systems that have strong advantages to vote strategically should be analyzed in game theory framework (analyzing nash equilibria in payoff matrices defined by voter strategies)
It performs the same core sleigh of hand: it takes a very simple view of strategic voting, assuming a fixed share of the electorate vote "strategically" regardless of election method, and making big assumptions about what's a good strategy.
That is, to put it mildly, not a reasonable assumption. It varies widely how much information about other people's preferences you need to "vote strategically", and the strategies also vary widely in how risky they are. If I have false beliefs about other people's preferences, how likely is it that I shoot myself in the foot with "strategic" voting? And how likely is it that we get caught in a bad equilibrium where our false beliefs about the other side's preferences reinforce each other?
All this makes the sort of modelling attempted here a vain pursuit. You just can't model strategy this naively.
But some methods come MUCH better out of this hopelessly naive modelling of strategy than others.
For instance, Approval voting requires very little information about other people's beliefs to vote strategically - you just need to know who the top two contenders are - The strategy is to approve the "least evil" of those two, plus any from the rest of the field you prefer to those two. It degenerates to pretty much the same problem as Plurality voting, with maybe slightly better chance to get out of bad equilibriums in the long run.
And Range/Score voting is even more extreme: you can vote strategically there even knowing nothing about other people's preferences. Just always use extreme values (0 and 100).
By comparison, strategic voting in Condorcet systems requires really exact information about the electorate's full range of preferences - and even then, you usually need to coordinate your strategic voting without the opposition getting wind of it, otherwise they can counter it. It's just not practical.
(Likewise, Borda gets a bad rap in these comparisons. It's not a good system, but the likelihood that "strategic voting" will backfire horribly means that in all likelihood, voters would not pursue those strategies. )